QT                   package:mgcv                   R Documentation

_Q_T _f_a_c_t_o_r_i_s_a_t_i_o_n _o_f _a _m_a_t_r_i_x

_D_e_s_c_r_i_p_t_i_o_n:

     If A is an r by c matrix,  where r<c, then it can be factorised: 
     AQ=[0,T] ,  where Q is an orthogonal matrix and T is reverse lower
     triangular. The first c-r columns of Q  from an orthogonal basis
     for the null space of A. Q is  returned as a sequence of r
     Householder rotations (from the right), as  described below.

_U_s_a_g_e:

     QT(A)

_A_r_g_u_m_e_n_t_s:

       A: is an R matrix having more columns than rows 

_D_e_t_a_i_l_s:

     This function is primarily useful for providing the null space of
     the  linear constraint matrix C, from the linear constraints  Cp=0
     , as a series of Householder rotations of the form  used
     internally by 'mgcv()'. It does not need to be called to set up a
     problem  for solution by mgcv.

_V_a_l_u_e:

     The returned matrix R, say, is of the same dimension as the input 
     matrix A. Each of its rows contains a vector, u_i ,  defining one
     Householder rotation, H_i = (I - u_i u_i') . The orthogonal matrix
     Q is  defined by: Q=H_1 H_2 ...  H_r .

_A_u_t_h_o_r(_s):

     Simon N. Wood simon@stats.gla.ac.uk

_R_e_f_e_r_e_n_c_e_s:

     Gill, Murray and Wright (1981) Practical Optimization, Academic 
     Press

_E_x_a_m_p_l_e_s:

     set.seed(0)
     y<-rnorm(12,1,1)
     A<-matrix(y,2,6)
     B<-QT(A)

